Junior Fellow of the Simons Society of Fellows

Department of Mathematics at Columbia University

2990 Broadway, New York, NY 10027, USA

**Email**: lctsai.math@gmail.com

My curriculum vitae.

I am a Junior Fellow of the Simons Society of Fellows, working with Ivan Corwin in the Department of Mathematics at Columbia University in the City of New York.

I am co-organizing the Columbia Probability Seminar.

I received my PhD in Mathematics at Stanford University in 2016, with my PhD advisor Amir Dembo.

My research interest lies in probability theory, particularly asymptotic behaviors of interacting particle systems, with a focus on their interplay between partial differential equations, stochastic partial differential equations, and integrability.

- NSF Grant No. DMS-1712575, 2017
- Junior Fellow, Simons Society of Fellows, 2016
- Graduate Fellow, Kavli Institute for Theoretical Physics, 2015

See also Google Scholar.

- Exact lower tail large deviations of the KPZ equation [arXiv]

Submitted - SPDE Limit of Weakly Inhomogeneous ASEP [arXiv]

with Ivan Corwin. Submitted - Stochastic PDE Limit of the Six Vertex Model [arXiv]

with Ivan Corwin, Promit Ghosal, and Hao Shen. Submitted

- Another look into the Wong-Zakai Theorem for Stochastic Heat Equation [arXiv]

with Yu Gu. To appear in Ann. Appl. Probab. - Stochastic Telegraph Equation Limit for the Stochastic Six Vertex Model [arXiv]

with Hao Shen. transaction of AMS 147(6) 2685–2705, 2019 - Exceedingly Large Deviations of the Totally Asymmetric Exclusion Process [arXiv]

with Stefano Olla. Electron. J. Probab. 24 (16), 2019 - Criticality of a randomly-driven front [arXiv][SN SharedIt]

with Amir Dembo. Arch. Rational Mech. Anal. (first online) - Coulomb-gas electrostatics controls large fluctuations of the KPZ equation [arXiv]

with Ivan Corwin, Promit Ghosal, Alexandre Krajenbrink, and Pierre Le Doussal.

Phys. Rev. Lett. 121, 060201 (2018) - Stationary Distributions of the Atlas Model [arXiv]

Electron. C. Probab. 23 (10), 2018 - ASEP(q,j) converges to the KPZ equation [arXiv]

with Ivan Corwin and Hao Shen. Ann. Inst. Henri Poincare (B) Probab. Stat. 54(2) 995-1012, 2018 - Optimal Surviving Strategy for Drifted Brownian Motions with Absorption [arXiv]

with Wenpin Tang. Ann. Prob. 46 (3) 1597-1650, 2018 - Stationary Gap Distributions for Infinite Systems of Competing Brownian Particles [arXiv][MR]

with Andrey Sarantsev. Electron. J. Probab. 22 (56), 2017 - Equilibrium Fluctuation of the Atlas Model [arXiv][MR]

with Amir Dembo. Ann. Prob. 45 (6B) 4529-4560, 2017 - KPZ equation limit of higher-spin exclusion processes [arXiv][MR]

with Ivan Corwin. Ann. Prob. 45 (3) 1771-1798, 2017 - Infinite Dimensional Stochastic Differential Equations for Dyson's Model [arXiv][MR][SN SharedIt]

Probab. Theory Related Fields. 166 (3) 801-850, 2016 - Weakly asymmetric non-simple exclusion process and the KPZ equation [arXiv][MR]

with Amir Dembo. Comm. Math. Phys. 341 (1), 219-261, 2016 - Equilibrating effects of boundary and collision in rarefied gases [MR]

with Hung-Wen Kuo and Tai-Ping Liu. Comm. Math. Phys. 328 (2), 421-480, 2014 - Free molecular flow with boundary effect [MR]

with Hung-Wen Kuo and Tai-Ping Liu. Comm. Math. Phys. 318 (2), 375-409, 2013 - Viscous shock propagation with boundary effect [MR]

Bull. Inst. Math. Acad. Sin. (N.S.) 6, 1-26, 2011

- Fall 2017-18, MATH 1102: Calculus II